Subject: Maths, asked on 20/5/18

## How to break (k^3 +6k^2+9k+4) this such that it becomes (k+1)(k+1)(k+4).

Subject: Maths, asked on 28/4/18

## Experts kindly help Subject: Maths, asked on 14/4/18

## Q. Find the differentiation

Subject: Maths, asked on 23/3/18
Subject: Maths, asked on 6/3/18

## Prove by PMI $3.{2}^{2}+{3}^{2}.{2}^{3}+...........+{3}^{n}{2}^{n+1}=\frac{12}{5}\left({6}^{n}-1\right)$prove

Subject: Maths, asked on 27/2/18

## Q.4. Prove that ${3}^{3n}-26n-1$ is divisible by 676.

Subject: Maths, asked on 14/2/18

## TELL ME THE ANSWER FOR 15th QUESTION . PLEASE TELL  ME FAST   Q15. Prove that ( cos )n = cos , for all n $\in$ N by using PMI.

Subject: Maths, asked on 8/2/18

## Using PMI prove that 1 × 1! + 2 × 2! + 3 × 3! + -----+ n × n! = (n + 1)! – 1 for all n∈N

Subject: Maths, asked on 31/1/18

## Experts,explain the one underlined after

Subject: Maths, asked on 31/1/18

## prove that 1+2+3+....+n=n(n+1)/2 by pmi

Subject: Maths, asked on 20/1/18

## Please solve it using mathematical induction

Subject: Maths, asked on 2/1/18

## Q. if a, b, c, are in A.P. , then

Subject: Maths, asked on 25/11/17

## Q. Prove that Please explain the last line of solution

Subject: Maths, asked on 25/11/17

## How is the underlined step coming?

Subject: Maths, asked on 25/11/17

## Prove the following by the principle of mathematical induction. 2n?>?n2, where?n?is a positive integer such that?n?> 4. Solution: Let the given statement be P(n), i.e., P(n) : 2n?>?n2?where?n?> 4 For?n?= 5, 25?= 32 and 52?= 25 ?25?> 52 Thus, P(n) is true for?n?= 5. Let P(n) be true for?n?=?k, i.e., 2k?>?k2?? (1) Now, we have to prove that P(k? 1) is true whenever P(k) is true, i.e. we have to prove that 2k? 1?> (k? 1)2. From equation (1), we obtain 2k?>?k2 On multiplying both sides with 2, we obtain 2 ? 2k?> 2 ??k2 2k? 1?> 2k2 ?To prove 2k? 1?> (k? 1)2, we only need to prove that 2k2?> (k? 1)2. Let us assume 2k2?> (k? 1)2. ? 2k2?>?k2? 2k? 1 ??k2?> 2k? 1 ??k2?? 2k?? 1 > 0 ? (k?? 1)2?? 2 > 0 ? (k?? 1)2?> 2, which is true as?k?> 4 Hence, our assumption 2k2?> (k? 1)2?is correct and we have 2k? 1?> (k? 1)2. Thus, P(n) is true for?n?=?k? 1. Thus, by the principle of mathematical induction, the given mathematical statement is true for every positive integer?n. ? IN THIS EXAMPLE IT HAS BEEN WRITTEN THAT , To prove 2k? 1?> (k? 1)2, we only need to prove that 2k2?> (k? 1)2. how?2k? 1?> (k? 1)2?=?2k2?> (k? 1)2 I cant understand how so plz explain that

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